Dekomposisi Model Proses Bisnis Tebang Muat Angkut (TMA) Menggunakan Refined Process Structure Tree (RPST) dan Metrik Kompleksitas

Abstract— In an organization, some problems often arise, one of which lies in the complexity of business process modeling. In business processes, high complexity values ​​are complicated to analyze and maintain as a whole, so a method is needed to break down the business process into smaller parts called the fragment process model. Therefore, a decomposition was carried out to decompose the process model to make it simpler. The benefit of decomposition is to make it easier for users to compose the required business process model. We used three different scenarios for the TMA process model to analyze each fragment. There is a process model with scenarios that tend to be the sequence, multi-branching, and nested branching. Furthermore, to support the results of the RPST, the calculation of the average complexity value with the Yaqin Complexity formula, and the standard deviation for the process model fragment was also carried out. Our experimental results found that the rate of the tree at the RPST affected the number of fragments. Also, we found that the more profound the tree depth, the higher the average complexity value. In this study, we found that scenarios that tend to be sequential, have the lowest average complexity value with the number 22, and a standard deviation value of 5,567. While the highest value is in the scenario that has nested branching, and there is a repetition process with an average complexity value of 29.8 and a standard deviation value of 13.405. Keywords— Process Model, RPST, Decomposition, Complexity Matrix, Standard Deviation. Abstrak— Dalam suatu organisasi seringkali timbul beberapa permasalahan, salah satunya terletak pada kompleksitas pemodelan proses bisnis. Dalam proses bisnis, nilai kompleksitas yang tinggi rumit untuk dianalisis dan dipelihara secara keseluruhan, sehingga diperlukan metode untuk memecah proses bisnis menjadi bagian-bagian yang lebih kecil yang disebut model proses fragmen. Oleh karena itu, dekomposisi dilakukan untuk menguraikan model proses agar lebih sederhana. Manfaat dekomposisi adalah memudahkan pengguna untuk menyusun model proses bisnis yang dibutuhkan. Kami menggunakan tiga skenario berbeda untuk model proses TMA untuk menganalisis setiap fragmen. Terdapat model proses dengan skenario yang cenderung berurutan, bercabang banyak, dan bercabang bersarang. Selanjutnya untuk mendukung hasil RPST juga dilakukan perhitungan nilai kompleksitas rata-rata dengan rumus Yaqin Complexity, dan standar deviasi untuk fragmen model proses. Hasil eksperimental kami menemukan bahwa laju pohon di RPST memengaruhi jumlah fragmen. Selain itu, kami menemukan bahwa semakin mendalam kedalaman pohon, semakin tinggi nilai kompleksitas rata-ratanya. Pada penelitian ini ditemukan skenario yang cenderung berurutan, memiliki nilai rata-rata kompleksitas terendah dengan angka 22, dan nilai standar deviasi 5,567. Sedangkan nilai tertinggi ada pada skenario bercabang nested, dan terjadi proses pengulangan dengan nilai kompleksitas rata-rata 29,8 dan nilai standar deviasi 13,405. Keywords—Model Proses, RPST, Dekomposisi, Matrik Kompleksitas, Standar Deviasi.

Regular finite decomposition complexity

We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov’s finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient Permanence. We show that for a collection containing all metric families with finite asymptotic dimension, all other permanence properties follow from Fibering Permanence.

Addendum to Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory (J. reine angew. Math. 694 (2014), 129–178)

We supply an argument that was missing from the proof of the main result of the article “Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory” [7]. The argument is essentially formal, and does not affect the strategy of the proof.

Burghelea conjecture and asymptotic dimension of groups

We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum–Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which together imply the Burghelea conjecture for such groups. We prove both conjectures for many classes of groups. It is known that the Burghelea conjecture does not hold for all groups, although no finitely presentable counterexample was known. We construct a finitely presentable (even type [Formula: see text]) counterexample based on Thompson’s group [Formula: see text]. We construct as well a finitely generated counterexample with finite decomposition complexity.